Finding acceleration and force of pulling

[Whitishcube]

Homework Statement

a window washer pulls herself up using a single pulley by pulling on the rope tied to the bucket she is in. the combined mass of the bucket and the washer is 72kg. a)how hard must she pull downward to be lifted at a constant speed? b) if this force is increased by 15%, what will her acceleration be?

Homework Equations

F_net= ma

The Attempt at a Solution

so part a was pretty easy. after setting up two freebody diagrams, i have
F_(net person)=F_tension - mg = ma
and
F_(net of hand pulling)= F_t - F_Pull = Ma?

one problem i had was knowing what the second freebody diagram is... i know the first one is the washer in the bucket, but I am not sure if the second one is the hand pulling on the rope (where the hand is the object), or if its the rope itself, in which case the force of the hand is what's pulling down and the tension upwards.
either way, i solved both equations for F_t (force of tension) by setting both of them equal to zero (due to constant velocity meaning 0 acceleration) and solved for the F_pull (the force of the person pulling).
so i get: F_pull = 705.6 N

for part b, i multiply the F_p by 1.15 for the 15% extra force. this gives me F_p=811.44 N.
from there i set up my two free body diagrams again and got:
F_t - mg = ma
and
F_t - F_p = M(-a)

plugging in 72kg for m gives F_t = 72a + 705.6.
the second part confuses me again. I am not sure what the mass would be in the second case. so i used the mass of the person (72kg) as M and solved for a.
on a side note, the acceleration in the second equation is negative because of the way i chose my axes and because of the direction of the acceleration.

then i plugged in F_t into the other equation, yielding:
72a + 705.6 - 811.44 = -72a
solving for a gives: a = 0.74 m/s^2

Any advice that could be given on this type of problem would be great. usually i could do this if i were given some other object that was tied to the rope instead of the person pulling on it. Thanks

 

[Whitishcube]

nevermind. i figured it out a much simpler way

 

[PhanthomJay]

You can't draw a FBD of the person without including the unknown normal force acting on the person from the bucket. Instead, draw a FBD that cuts through both ropes and encircles the bucket with person in it, then use Newton 1 for part a.

Edit, oh, nevermind, I see you got it, good.